Resources

Web Resources

Free Online Solvers

AMPL online : Create AMPL files off-line, then upload and solve them at this site. A variety of solvers can be selected, including MINOS, SNOPT, Lancelot and others. Limited to 300 variables and 300 constraints and 30 seconds of execution time.

NEOS: The Network-Enabled Optimization System. An online system for submitting and solving optimization problems including LP, MIP, NLP, etc.

Optimization as an Internet Resource: paper in pdf format that includes numerous useful links to web resources for optimization.

Wikipedia list of optimization software, some of which are free.


Free Student/Trial Editions of Commercial Solvers for LP/MILP/QP

Cplex: from IBM. Can also download the Optimization Studio for model creation. Associated free courses.

Gurobi: also includes a mixed-integer quadratic programming solver.

MOSEK: also has a very nice Matlab Toolbox interface.

XPress: includes a nonlinear solver.


Downloadable Modelling Systems That Include Free Solvers

AIMMS: student edition licenses are here.

AMPL: Student editions of the AMPL modelling system for various platforms. Demo-size editions of various commercial solvers are included in the download.

GAMS: The original modelling "general algebraic modelling language". Academic and trial licenses available here.

LINDO: Student editions of LP, NLP, and MILP solvers, plus the LINGO modelling language. Limited to 150 constraints and 300 variables. Windowed interface. The classic LINDO is easy to use and suitable for homework assignments.  Look for it on the downloads page: a manual is also available there. Classic LINDO is not available for the Macintosh; Mac users should download LINGO, a system that includes a modelling language and associated solvers.

Maximal: Student edition of the Maximal Software modelling system (MPL) coupled with a student edition of the CPLEX LP/MILP solver. Windowed interface. Limited to 300 variables and 300 constraints.


Free and Open Source Linear Programming Codes:

COIN-OR: http://www.coin-or.org/projects/ has links to the CLP solver as well as many others for several classes of optimization problems.

GLOP is Google's open-source LP code.

GLPK: http://www.gnu.org/software/glpk/.  GLPK is also available embedded in Octave, a free and open source MATLAB clone, at http://www.gnu.org/software/octave/.

QSOPT: http://www.isye.gatech.edu/~wcook/qsopt/

SOPLEX: http://soplex.zib.de/


Free and Open Source Mixed-Integer Linear Programming Codes

CBC: http://www.coin-or.org/projects/. CBC is a MIP framework that works with the CLP LP solver.

GLPK: http://www.gnu.org/software/glpk/glpk.html. MIP capability is built into GLPK. GLPK is also available embedded in Octave, a free and open source MATLAB clone, at http://www.gnu.org/software/octave/.

LP_SOLVE: http://lpsolve.sourceforge.net/. MIP capability is built into the LP_SOLVE.

MINTO: http://coral.ie.lehigh.edu/~minto/.  MINTO is a MIP framework which requires that a separate LP solver be attached.

SCIP: http://scip.zib.de/.  SCIP is a MIP framework which requires that a separate LP solver be attached. SCIP also incorporates many concepts from constraint programming.

SYMPHONY: http://www.coin-or.org/projects/SYMPHONY.xml.  SYMPHONY is a MIP framework that works with the CLP LP solver.


Solvers That You May Already Have Access to:

LP, mixed-integer programming, and nonlinear solvers are included in software that you already have. You can find solvers in MS-Excel, Google Sheets, Matlab, and Octave.


Solver Comparisons:

See Hans Mittelmann's benchmarks comparing commercial and non-commercial solvers in many categories to find the one that will work best for you.


Tutorials, Textbooks, Problem Sets:

Optimization101.org (this site).

Advice on formulating linear programs by using building blocks called formulettes.

The linear programming FAQ page.  Includes pointers to software, test models, etc.

The nonlinear programming FAQ page. Includes pointers to software, test models, etc.

The glossary of mathematical programming terms, many not found in standard dictionaries of mathematics.

Spreadsheet Optimization: By Frontline Systems, which markets add-in solvers for Microsoft Excel.

Optimization Modelling: By Maximal Software, which markets the MPL language and attached solvers.

JE Beasley's Tutorial questions and solutions.  See also Beasley's past exams without solutions.

Bob Vanderbei's online LP book and exercises.


Current as at March 10, 2021. Optimization101.org homepage.


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Contents

Chapter 1: Introduction.  An introduction to the process of optimization and an overview of the major topics covered in the course.  Last revision: December 2020 . Chapter 2: Introduction to Linear Programming.  The basic notions of linear programming and the simplex method. The simplex method is the easiest way to provide a beginner with a solid understanding of linear programming.  Last revision: December 2020. See animation  LP1 . A good  article on formulating LPs  by Gerry Brown and Rob Dell. Example questions with solutions . March 4, 2021. Chapter 3: Towards the Simplex Method for Efficient Solution of Linear Programs.  Cornerpoints and bases. Moving to improved solutions.  Last revision: December 2020 . See animation  LP2 . Chapter 4: The Mechanics of the Simplex Method.  The tableau representation as a way of illustrating the process of the simplex method. Special cases such as degeneracy and unboundedness.  Last revision: December 2020. See animation  LP3 . Example questions
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